Ion dynamics near charged electrodes with excluded volume effect

Author

Baker-Jarvis, James ; Riddle, Bill ; Young, Albert M.

Author_Institution

Div. of Radio-Frequency Technol., Nat. Inst. of Stand. & Technol., Boulder, CO, USA

Volume

6

Issue

2

fYear

1999

fDate

4/1/1999 12:00:00 AM

Firstpage

226

Lastpage

235

Abstract

The goal of this paper is to analyze ion relaxation around a charged electrode taking into account finite ion volume and frequency. Time-dependent and electrostatic equations for ion behaviour near an electrode are developed and include the effects of nonequilibrium and steric hindrance. Time-dependent wave equations for the potentials are developed in the Lorentz gauge. The charge density is expressed as a sum of the quasi-steady state solution plus a nonequilibrium term. For slowly changing potentials the ions are in quasi-equilibrium and we show that in this limit the potential satisfies the sinh-Gordon equation. New solutions to this nonlinear time-dependent equation are developed. In the low voltage limit the equation reduces to the Klein-Gordon equation, time-dependent analog of the Debye-Huckel equation. We also present equations for capacitance and surface charge

Keywords

Boltzmann equation; Poisson equation; capacitance; electrochemical electrodes; electrostatics; ion mobility; sine-Gordon equation; surface charging; Klein-Gordon equation; Lorentz gauge; capacitance; charged electrodes; electrostatic equations; excluded volume effect; finite ion volume; ion behaviour; ion dynamics; ion relaxation; nonequilibrium effects; nonlinear time-dependent equation; quasi-steady state solution; sinh-Gordon equation; steric hindrance; surface charge; time-dependent equations; time-dependent wave equations; Capacitance; Current density; Differential equations; Electrodes; Electrostatics; Integral equations; Nonlinear equations; Partial differential equations; Poisson equations; Radio frequency;

fLanguage

English

Journal_Title

Dielectrics and Electrical Insulation, IEEE Transactions on

Publisher

ieee

ISSN

1070-9878

Type

jour

DOI

10.1109/94.765913

Filename

765913